{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:4TIKCLE3MYFH3GEFV4X726DVMG","short_pith_number":"pith:4TIKCLE3","canonical_record":{"source":{"id":"2006.14010","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.PL","submitted_at":"2020-06-24T19:27:24Z","cross_cats_sorted":[],"title_canon_sha256":"88494eb90f0f269eaf60eca20112e38c46ccdf79da6b835d96caaf58b8bc9901","abstract_canon_sha256":"073b2997d7ea7420b75eeb29316ee4796ae8aae92095d43c3b4a95fdb27a6951"},"schema_version":"1.0"},"canonical_sha256":"e4d0a12c9b660a7d9885af2ffd7875618b7aaac7a62a8b5750490b5248f3fb6d","source":{"kind":"arxiv","id":"2006.14010","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2006.14010","created_at":"2026-07-05T01:37:12Z"},{"alias_kind":"arxiv_version","alias_value":"2006.14010v2","created_at":"2026-07-05T01:37:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2006.14010","created_at":"2026-07-05T01:37:12Z"},{"alias_kind":"pith_short_12","alias_value":"4TIKCLE3MYFH","created_at":"2026-07-05T01:37:12Z"},{"alias_kind":"pith_short_16","alias_value":"4TIKCLE3MYFH3GEF","created_at":"2026-07-05T01:37:12Z"},{"alias_kind":"pith_short_8","alias_value":"4TIKCLE3","created_at":"2026-07-05T01:37:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:4TIKCLE3MYFH3GEFV4X726DVMG","target":"record","payload":{"canonical_record":{"source":{"id":"2006.14010","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.PL","submitted_at":"2020-06-24T19:27:24Z","cross_cats_sorted":[],"title_canon_sha256":"88494eb90f0f269eaf60eca20112e38c46ccdf79da6b835d96caaf58b8bc9901","abstract_canon_sha256":"073b2997d7ea7420b75eeb29316ee4796ae8aae92095d43c3b4a95fdb27a6951"},"schema_version":"1.0"},"canonical_sha256":"e4d0a12c9b660a7d9885af2ffd7875618b7aaac7a62a8b5750490b5248f3fb6d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:37:12.316792Z","signature_b64":"ILPCC9XcN3XARAWnXMgb5Q8ew9eAE5Y/BZE3dV89r6VpM5eAheaYUxTQPTeNs+D35JT5Jm9td/nWpEt+bNKuDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e4d0a12c9b660a7d9885af2ffd7875618b7aaac7a62a8b5750490b5248f3fb6d","last_reissued_at":"2026-07-05T01:37:12.316303Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:37:12.316303Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2006.14010","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T01:37:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"25ShFFyN97DfkwU/PnL6M2n/EDB8wbaf2bj817QhYYwyEEfz0ay8PVhkyUMXJ7Vh2q+Am3kPE1wC1DnCgQI/BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T19:38:07.984412Z"},"content_sha256":"da7fe8bcc1c34009b7948347a202c8f38efd544e5d9df2f800fd28f94805ea12","schema_version":"1.0","event_id":"sha256:da7fe8bcc1c34009b7948347a202c8f38efd544e5d9df2f800fd28f94805ea12"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:4TIKCLE3MYFH3GEFV4X726DVMG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Raising Expectations: Automating Expected Cost Analysis with Types","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.PL","authors_text":"David M Kahn, Di Wang, Jan Hoffmann","submitted_at":"2020-06-24T19:27:24Z","abstract_excerpt":"This article presents a type-based analysis for deriving upper bounds on the expected execution cost of probabilistic programs. The analysis is naturally compositional, parametric in the cost model, and supports higher order functions and inductive data types. The derived bounds are multivariate polynomials that are functions of data structures. Bound inference is enabled by local type rules that reduce type inference to linear constraint solving. The type system is based on the potential method of amortized analysis and extends automatic amortized resource analysis (AARA) for deterministic pr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2006.14010","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2006.14010/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T01:37:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ck8jldtKKzQUsPYBP6ClxUfQHnHjc96KNWEuwnqkBoXLbiqs+zzQ9OrJ1WSKXjmKDnNrUQC/t7BqaNMxmBiKAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T19:38:07.985301Z"},"content_sha256":"68ab541af6d3a005e73eb178ae0d3eb9c33317129bb31af3405d291bddfe905a","schema_version":"1.0","event_id":"sha256:68ab541af6d3a005e73eb178ae0d3eb9c33317129bb31af3405d291bddfe905a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4TIKCLE3MYFH3GEFV4X726DVMG/bundle.json","state_url":"https://pith.science/pith/4TIKCLE3MYFH3GEFV4X726DVMG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4TIKCLE3MYFH3GEFV4X726DVMG/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-21T19:38:07Z","links":{"resolver":"https://pith.science/pith/4TIKCLE3MYFH3GEFV4X726DVMG","bundle":"https://pith.science/pith/4TIKCLE3MYFH3GEFV4X726DVMG/bundle.json","state":"https://pith.science/pith/4TIKCLE3MYFH3GEFV4X726DVMG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4TIKCLE3MYFH3GEFV4X726DVMG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:4TIKCLE3MYFH3GEFV4X726DVMG","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"073b2997d7ea7420b75eeb29316ee4796ae8aae92095d43c3b4a95fdb27a6951","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.PL","submitted_at":"2020-06-24T19:27:24Z","title_canon_sha256":"88494eb90f0f269eaf60eca20112e38c46ccdf79da6b835d96caaf58b8bc9901"},"schema_version":"1.0","source":{"id":"2006.14010","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2006.14010","created_at":"2026-07-05T01:37:12Z"},{"alias_kind":"arxiv_version","alias_value":"2006.14010v2","created_at":"2026-07-05T01:37:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2006.14010","created_at":"2026-07-05T01:37:12Z"},{"alias_kind":"pith_short_12","alias_value":"4TIKCLE3MYFH","created_at":"2026-07-05T01:37:12Z"},{"alias_kind":"pith_short_16","alias_value":"4TIKCLE3MYFH3GEF","created_at":"2026-07-05T01:37:12Z"},{"alias_kind":"pith_short_8","alias_value":"4TIKCLE3","created_at":"2026-07-05T01:37:12Z"}],"graph_snapshots":[{"event_id":"sha256:68ab541af6d3a005e73eb178ae0d3eb9c33317129bb31af3405d291bddfe905a","target":"graph","created_at":"2026-07-05T01:37:12Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2006.14010/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This article presents a type-based analysis for deriving upper bounds on the expected execution cost of probabilistic programs. The analysis is naturally compositional, parametric in the cost model, and supports higher order functions and inductive data types. The derived bounds are multivariate polynomials that are functions of data structures. Bound inference is enabled by local type rules that reduce type inference to linear constraint solving. The type system is based on the potential method of amortized analysis and extends automatic amortized resource analysis (AARA) for deterministic pr","authors_text":"David M Kahn, Di Wang, Jan Hoffmann","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.PL","submitted_at":"2020-06-24T19:27:24Z","title":"Raising Expectations: Automating Expected Cost Analysis with Types"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2006.14010","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:da7fe8bcc1c34009b7948347a202c8f38efd544e5d9df2f800fd28f94805ea12","target":"record","created_at":"2026-07-05T01:37:12Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"073b2997d7ea7420b75eeb29316ee4796ae8aae92095d43c3b4a95fdb27a6951","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.PL","submitted_at":"2020-06-24T19:27:24Z","title_canon_sha256":"88494eb90f0f269eaf60eca20112e38c46ccdf79da6b835d96caaf58b8bc9901"},"schema_version":"1.0","source":{"id":"2006.14010","kind":"arxiv","version":2}},"canonical_sha256":"e4d0a12c9b660a7d9885af2ffd7875618b7aaac7a62a8b5750490b5248f3fb6d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e4d0a12c9b660a7d9885af2ffd7875618b7aaac7a62a8b5750490b5248f3fb6d","first_computed_at":"2026-07-05T01:37:12.316303Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:37:12.316303Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ILPCC9XcN3XARAWnXMgb5Q8ew9eAE5Y/BZE3dV89r6VpM5eAheaYUxTQPTeNs+D35JT5Jm9td/nWpEt+bNKuDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T01:37:12.316792Z","signed_message":"canonical_sha256_bytes"},"source_id":"2006.14010","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:da7fe8bcc1c34009b7948347a202c8f38efd544e5d9df2f800fd28f94805ea12","sha256:68ab541af6d3a005e73eb178ae0d3eb9c33317129bb31af3405d291bddfe905a"],"state_sha256":"d9205f92717feb93cf18b4d7181e7cd37191bd58706d83df3419b6f1ab0054bc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"o1Eg/naODhzkAdz4jgB7923uLBAy7qGPyeQHaHg9eqQk3Pj9N1kXe+/yKeUqzyiVV5GVX/6yxJQNqgaFl9uJBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-21T19:38:07.992264Z","bundle_sha256":"e04c831c727895f9dbd5b1e08eceda0cbe5cd354fbfa89d162ba1cd478ef3a98"}}